Question

Inequality of Lebesgue integrals

score 83 · Answer 1 · 2026-04-15 05:14:05

83

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Inequality of Lebesgue integrals

Published on 15 Apr 2026 - 5:14

score 57 · Answer 2 · 2026-04-16 00:00:36

57

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Helping understand line integral $\int_{K,+}{(x+y)}dx+(y-x)dy$

Published on 16 Apr 2026 - 0:00

score 106 · Answer 3 · 2026-04-14 04:31:02

106

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Approximate an integrable function using a simple function (Proving existance)

Published on 14 Apr 2026 - 4:31

score 739 · Answer 4 · 2026-04-16 06:54:05

739

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Part of proof to show Lebesgue-lebesgue measurable

Published on 16 Apr 2026 - 6:54

score 215 · Answer 5 · 2026-04-16 09:16:39

215

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Proving that $\left|\int_{a}^{b}\frac{\sin(x)}{x}dx\right|\leq 3$, given $1\leq a<b$

Published on 16 Apr 2026 - 9:16

score 406 · Answer 6 · 2026-04-24 02:32:34

406

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Prove series converge for almost every $x$

Published on 24 Apr 2026 - 2:32

score 31 · Answer 7 · 2026-04-15 03:16:19

31

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Compute $\int_{B(0,2)} (xy^2+y^2z)d\mu(x,y,z)$ where $\mu$ is defined by an another integral

Published on 15 Apr 2026 - 3:16

score 2k · Answer 8 · 2026-04-15 16:17:47

2k

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If $f:\mathbb{R}\to[0, \infty)$ (uniformly) continuous and $f \in L^1$, then $\lim_{x\to\pm\infty}f(x)=0$?

Published on 15 Apr 2026 - 16:17

score 1.7k · Answer 9 · 2026-04-16 12:12:07

1.7k

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Prove that $F(x,y)=f(x-y)$ is Borel measurable

Published on 16 Apr 2026 - 12:12

score 3k · Answer 10 · 2026-04-15 23:59:30

3k

Views

Show that $\int_{0}^{\infty}x^ne^{-x}\,dx=n!$ by differentiating the equality $\int_{0}^{\infty}e^{-tx}\,dx=\frac{1}{t}$

Published on 15 Apr 2026 - 23:59

score 208 · Answer 11 · 2026-04-12 11:06:09

208

Views

Shortest Proof of Lebesgue Dominated Convergence Theroem ( 5 lines) without using Fatou's lemma

Published on 12 Apr 2026 - 11:06

score 308 · Answer 12 · 2026-04-09 19:29:29

308

Views

An integrally defined borel measurable function

Published on 09 Apr 2026 - 19:29

score 100 · Answer 13 · 2026-04-17 11:06:51

100

Views

Show that $\int\vert \int f(y)g(x-y)\,dy \rvert \,dx \le \iint \vert f(y)g(x-y)\rvert\, dy\, dx$

Published on 17 Apr 2026 - 11:06

score 1.2k · Answer 14 · 2026-04-13 20:27:26

1.2k

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Converse for Fubini-Tonelli's theorem

Published on 13 Apr 2026 - 20:27

score 415 · Answer 15 · 2026-04-16 07:54:20

415

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Let $f:\mathbb{R}\to[0,\infty)$ measurable and $f\in L^1$. Show that $\mu(E)<\delta \implies \int_E f < \varepsilon$.

Published on 16 Apr 2026 - 7:54

List Question

Inequality of Lebesgue integrals

Helping understand line integral $\int_{K,+}{(x+y)}dx+(y-x)dy$

Approximate an integrable function using a simple function (Proving existance)

Part of proof to show Lebesgue-lebesgue measurable

Proving that $\left|\int_{a}^{b}\frac{\sin(x)}{x}dx\right|\leq 3$, given $1\leq a<b$

Prove series converge for almost every $x$

Compute $\int_{B(0,2)} (xy^2+y^2z)d\mu(x,y,z)$ where $\mu$ is defined by an another integral

If $f:\mathbb{R}\to[0, \infty)$ (uniformly) continuous and $f \in L^1$, then $\lim_{x\to\pm\infty}f(x)=0$?

Prove that $F(x,y)=f(x-y)$ is Borel measurable

Show that $\int_{0}^{\infty}x^ne^{-x}\,dx=n!$ by differentiating the equality $\int_{0}^{\infty}e^{-tx}\,dx=\frac{1}{t}$

Shortest Proof of Lebesgue Dominated Convergence Theroem ( 5 lines) without using Fatou's lemma

An integrally defined borel measurable function

Show that $\int\vert \int f(y)g(x-y)\,dy \rvert \,dx \le \iint \vert f(y)g(x-y)\rvert\, dy\, dx$

Converse for Fubini-Tonelli's theorem

Let $f:\mathbb{R}\to[0,\infty)$ measurable and $f\in L^1$. Show that $\mu(E)<\delta \implies \int_E f < \varepsilon$.

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